Answer 1:
The short answer is that cold orange juice will
have a higher pH (be less acidic) than room
temperature orange juice. Similarly, warm orange
juice will have a lower pH (be more acidic) than
room temperature orange juice. Here is
why: Orange juice, which generally has a pH
around 3.5, is acidic because it contains citric
acid. Citric acid is a weak acid which means that
it does not completely dissociate in water. The
behavior of weak acids can be described by an
equilibrium constant, Ka. Usually Ka is reported
as pKa, where pKa = log(Ka). The pKa for citric
acid is 3.13. Any weak acid, HA, when added
to water will partially dissociate into the
conjugate base, A, and H^{+} (or more
accurately H_{3}O^{+}). This
reaction is described by the following equilibrium
equation:HA > A^{} + H^{+}.The
equilibrium constant for this equation is:Ka =
[A^{}][H^{+}]/[HA] And the
pH is given by: pH = log[H^{+}]The
equilibrium constant, Ka, essentially tells us how
much of HA will dissociate and produce
H^{+}. The bigger Ka (or the smaller pKa),
the more H^{+} the acid will produce. In
order to figure out how the pH changes with
temperature, we need to figure out how Ka changes
with temperature. The vant Hoff equation
(which is derived from thermodynamics) tells us
that the change in Ka with temperature depends on
the enthalpy of the
reaction. lnK_{2}  lnK_{1}
=  H/R *(1/T_{2}1/T_{1})In
the above equation, K_{1} and
K_{2} are the equilibrium constants, R =
8.314 J/mol K is the gas constant, T_{1}
and T_{2} are the initial and final
temperatures, and H is the enthalpy of the
reaction. According to the National
Institute of Standards (NIST), the enthalpy of
dissociating in water (called the enthalpy of
ionization) for citric acid is 4.07 kJ/mol.
If we set K_{1} = Ka and T_{1}
= room temperature (25C or 298K), then we can pick
different values of T_{2} and see what
happens to K_{2}. K_{2} will be
the equilibrium constant at temperature
2. First we rearrange the
equation: lnK_{2} = lnK_{1} 
H/R *(1/T_{2}1/T_{1}) If we
pick T_{2} = 1C = 274K (just above the
freezing point of water), then we
findlnK_{2} = ln(0.00074) [(4070
J/mol)/(8.314 J/mol K)]*[(1/274K)
1/298K)]lnK_{2} = 7.21 0.144 =
7.354K_{2} = 0.000641 pK_{2} =
3.19Since K_{2} is less than Ka
(and pK_{2} is greater than pKa), then the
acid will not dissociate as much when the solution
is colder. That means there will not be as much
H^{+} present in the solution and the pH
will be higher. Now if we pick T_{2}
= 37C = 310K (about the temperature of the human
body), then we findlnK_{2} = ln(0.00074)
[(4070 J/mol)/(8.314 J/mol K)]*[(1/310K)
1/298K)]lnK_{2} = 7.21 (0.0636) =
7.15K_{2} = 0.000788 pK_{2} =
3.10 Since K_{2} is more than Ka (and
pK_{2} is less than pKa), then the acid
will dissociate more when the solution is warmer.
That means there will be more H^{+}
present in the solution and the pH will be
lower. An easier, but much less accurate way
to find the pKa at a different temperature is to
use the tabulated value of 0.002 pKa/T. This
means that for every 1C (1K) increase in
temperature, the pKa of citric acid will decrease
by approximately 0.002. What all of this
means for the overall pH is that, although it does
depend on temperature, there will only be very
small changes. It will not change by more than
approximately 0.04 in the temperature range
discussed here. Assuming that the orange juice
starts with a pH of 3.5 at room temperature, it
will stay between 3.46 and 3.54 over the
temperature range described above. Of
course, orange juice is not purely citric acid so
these calculations for citric acid only give us an
estimate for what will happen to the pH of orange
juice. The pH should follow the same trend as
predicted here, but the numbers might not be
exactly right. Also, keep in mind that this
is not true for all acids. Whether the pH
increases or decreases ultimately depends on the
value of H. If H for the given acid is positive as
in the case of citric acid, then that acid will
follow the same trend as citric acid. However, if
H is negative, then the pH will show the opposite
behavior. For these acids with negative enthalpy,
pH will increase with increasing temperature and
decrease with decreasing temperature. If
you try to measure the pH change of orange juice
with changing temperature with a pH meter, you
will measure a much bigger change than what is
predicted here. That is because the electrical
response of the pH meter also depends on
temperature so it is only calibrated pro
